give my eye teeth for

"The House of Silk" からの引用です。

A little common courtesy wouldn't have hurt, but that's the man we're up against. He's with Holmes now, interviewing him. I'd give my eye teeth to be in the room with them, for that would be a battle of wits if ever there was one.
"give my eye teeth" の意味を調べます。
・Collins Dictionary: If you say that you would give your eye teeth for something, you mean that you want it very much and you would do anything to get it.: She has the job most of us would give our eye teeth for.

・Macmillan Dictionary: used for saying that you wish you could have/do something very much: I’d give my eye teeth for a house like that.

・Dictionary.com: to give something one considers very precious, usually in exchange for an object or situation one desires: She would give her eyeteeth for that job.
ところで、"eye teeth" は犬歯を指しています。
The pointed long teeth — also called canines because they look a bit like those in dogs — are called eye teeth because the pair in the upper jaw lie directly below the eyes. （World Wide Wordsからの引用）